Towards an optimal design of acoustic Luneburg lenses

Although the concept of acoustic Luneburg lenses was first proposed more than 50 years ago, its physical realization became feasible only in the last decade, owing to advancements in metamaterials research. Since then, numerous studies have explored the potential of these devices from the acoustic perspective. However, a comprehensive understanding of the mechanisms associated with the optimal performance of these lenses remains underexplored in the literature. This study conducts numerical investigations to identify parameters enhancing acoustic gain in Luneburg lenses. The analyses are conducted with the results obtained from a flattened Luneburg lens model based on the lattice Boltzmann method. Results, scaled with the Helmholtz number, He, indicate that the maximum acoustic gain occurs at He = 1.3, with performance sustained over a wide range of Helmholtz values. Analysis of surface impedance reveals underperformance for Helmholtz values below 0.5 due to viscous dissipation and above 2.0 due to Bragg reflections. These results provide a basis for evaluating the Helmholtz parameters that optimize the acoustic gain of Luneburg lenses.